Method of postive fluid flow extrusion and optimum fluid control element therefor

ABSTRACT

The design and use of an optimum fluid control element for any positive fluid flow extrusion are set forth. The flow control surface of the fluid control element is sigmoidal with a critical clearance between the billet and the flow control surface occupied by pressurized fluid which exerts deformation pressures against the billet and accomplishes a portion of the work of deformation. The fluid occupies between about 3 and 10 percent of the cross-sectional area of the passage defined by the flow control surface through the fluid control element. Use of the fluid control element increases overall extrusion efficiency and homogeneous deformation is approached.

United States Patent Ahmed [451 July 18, 1972 [72] Inventor: Nazeer Ahmed, New Brunswick, NJ.

[73] Assignee: Western Electric Company, Incorporated,

New York, NY.

[22] Filed: Oct. 1, 1969 [21] Appl, No.: 862,765

[52] U.S. Cl ..72/60, 72/467, 72/271 [51] Int. Cl. ..B2lc 25/02 [58] Field of Search. ....72/60, 467

[56] References Cited UNITED STATES PATENTS 3,191,413 6/1965 Stulen ..72/467 2,245,608 6/1941 Rogers ...72/467 2,750,034 6/1956 Gersman... ...72/467 2,660,302 11/1953 Gersman ..72/467 3,157,274 11/1964 Kyle et a1 ...72/467 3,449,935 6/1969 McAllan ..72/60 FOREIGN PATENTS OR APPLICATIONS 257,366 9/1926 Great Britain ..72/467 OTHER PUBLICATIONS Beresnev et al.: Some Problems of Large Plastic Deformation" pp. 26- 54, 70- 74; 1963 The Macmillian Co., New York; Sci. Lib. No. TA 460 B45 Avitzur; Analysis of Wire Drawing and Extrusion Through Conical Dies of Large Cone Angle" pp. 305- 316; J. Engr. for Industry; Vol. 86 Series B No. 4; Nov. 1964; Sci. Lib. call No.TA1 J62 Primary Examiner-Richard J. Herbs! Attorney-W. M. Kain, R. C. Winter, J. B. Hoofnagle and J. Schuman ABSTRACT The design and use of an optimum fluid control element for any positive fluid flow extrusion are set forth. The flow control surface of the fluid control element is sigmoidal with a critical clearance between the billet and the flow control surface occupied by pressurized fluid which exerts deformation pressures against the billet and accomplishes a portion of the work of deformation. The fluid occupies between about 3 and 10 percent of the cross-sectional area of the passage defined by the flow control surface through the fluid control element. Use of the fluid control element increases overall extrusion efficiency and homogeneous deformation is approached.

3 Claims, 13 Drawing figures PAT ENIED JUL 1 8 m2 SHEET 3 OF 4 DIE ANGLE (DEGREES) DISTANCE 'ALONGD/E (INCHES) TY J o O 0 O 0 8 6 4 2 FIG.

PATENTED JUL] 8 I972 SHEET 0F 4 METHOD OF POSTIVE FLUID FLOW EXTRUSION AND OPTIMUM FLUID CONTROL ELEMENT THEREFOR BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates generally to the extrusion of material to form a product. More particularly, it relates to a method of extruding materials by a flow of pressurized fluid, the steps which must be taken to design an optimum fluid control element for a particular extrusion job, and the contour of the flow control surface of an optimum fluid control element.

Although the invention is useful for the deformation of virtually any deformable material, the invention will be described in terms of the extrusion of a metal billet to form a product, e.g., wire.

2. Prior Art The advantages of hydrostatic extrusion over conventional extrusion are well detailed in the literature and need not be discussed herein (see, for example, H. Ll. D. Pugh, Recent Developments in Cold Forming, Bullied Memorial Lectures, 1965, University of Nottingham, England). A proper understanding of the present invention does require a knowledge of the principles of hydrostatic extrusion, but this subject is more relevant when discussed with reference to the present invention, and is set forth in the Description of Embodiments below.

Two of the essential aspects of the present invention are the concept of an ideal or optimum fluid control element having a fluid control surface contoured for optimum results for a given extrusion job, and the concept of positive fluid flow through the fluid control element along with the extruding billet, which concept is disclosed broadly in copending US. application Ser. No. 862,677, filed Oct. 1, 1969, and assigned to the same assignee as the instant application.

An optimum fluid control element is a deforming agency which minimizes the work or energy necessary to extrude material to form a product. By comparison, an optimum deforming agency in the drawing arts, is embodied in a die for the drawing of strip materials as designed by Richmond et al. (A Die Profile For Maximum Efficiency In Strip Drawing," ASME Proceedings of the Fourth National Congress of Applied Mechanics, 1962). Richmond et al. disclose a single equation for the die profile, which is sigmoidal and has zero entrance and exit angles. This is possible because the strip is very wide compared to its thickness, and drawing can be safely assumed to occur under conditions of plane strain, i.e., the stress system is bi-axial. The die is shaped in such a way that the direction of flow in the plastic region is everywhere coincident with the direction of principal stress. With the added assumption of perfect lubrication, this die is capable of the same efficiency as uniform compression. While Richmond et al. suggest that their method is applicable to other steady state forming operations as well, this is not the case with extrusion, where axis symmetry rather than plane strain conditions exist, and the relevant stress system is tri-axial.

The idea of reducing the friction during extrusion must be as old as extrusion itself. The extrusion of many materials is essentially impossible without the use of lubricants. The lubricants used may be liquid (oils), viscous (greases) or solid (plated metals). Ordinary hydrostatic extrusion reduces friction as compared to conventional extrusion, since the billet is surrounded by a pressurized fluid and metal-to-metal contact takes place only in the die itself. Prior workers have advanced the concept of forced lubrication, wherein a film of the lubricant is forced through the die with the extruding billet, further reducing friction. This is discussed by Pugh, noted above, and by Avitzur in the articles cited below. This is relevant to positive fluid flow as set forth in the present invention, but only insofar as it relates to the concept of fluid being present within the fluid control element, which concept, as noted above, is broadly disclosed in copending US application Ser. No. 862,677.

Other prior art teachings are discussed hereinbelow where they may be useful to assist in the understanding of the present invention.

OBJECTS OF THE INVENTION The general objects of the invention are to provide an optimum fluid control element for any given positive fluid flow extrusion, and to provide a method of extruding material to form a product with this fluid control element.

Various other objects and advantages of the invention will become clear from the following description of embodiments thereof, and the novel features will be particularly pointed out in connection with the appended claims.

THE DRAWINGS In describing the invention reference will be made to the accompanying drawings, wherein:

FIG. 1 is a greatly simplified cross-sectional view of a conventional hydrostatic extrusion chamber;

FIG. 2 is a schematic representation of the forces acting on a segment of a billet in the fluid control element of the invention;

FIG. 3 is a plot showing the value of the sine of an angle from 0 to i.e., a sine curve;

FIG. 4 is a schematic representation of a collection of segments of the type shown in FIG. 2;

FIG. 5 is a plot of yield stress vs. reduction ratio for 99.9 percent aluminum;

FIG. 6 is a stress-strain curve for 99.9 percent aluminum showing the effect of varying strain rate at room temperature;

FIG. 7 is a plot of temperature vs. strain rate for 99.9 percent aluminum;

FIG. 8 shows two plots of pressure vs. flow control surface position, i.e. a pressure profile, for the extrusion of 99.9 percent aluminum at an extrusion ratio of about 68:] and a billet feed of 7 feet per minute;

FIG. 9 is a plot showing the effect of the surface angle a on various factors affecting the total work of deformation;

FIG. 10 is a profile of the flow control surface used in the extrusion of FIG. 8;

FIG. 11 is a plot of surface hardness vs. reduction ratio for 99.9 percent aluminum;

FIG. 12 is a simplified, cross-sectional view of extrusion equipment which can be used with the fluid control element and method of the invention; and

FIG. 13 is a schematic, cross-sectional view of a compound fluid control element.

DESCRIPTION OF EMBODIMENTS To facilitate a proper understanding of the invention, conventional hydrostatic extrusion is initially discussed, followed by a summary of the present invention, factors to be considered in design of the fluid control element, actual design of the optimum fluid control element by several methods, use of the fluid control element in a process of positive fluid flow extrusion, and a specific, working example.

Generally, the process of hydrostatic extrusion involves the use of a pressurized fluid acting on the billet to force it through a die, in place of the ram pressure of conventional extrusion processes. The fluid acts on the sides (radially) as well as the end (axially) of the workpiece and the pressure is sufficient to force the billet through the die, which is a conventional, conical die (referred to herein, for reasons which will become clear below, as a straight die). The foregoing is illustrated in FIG. 1. A die 10 has a cavity 12 filled with fluid 14. The fluid pressure P, acts in the axial direction on the end of the billet 16, pushing it through the die opening or throat 18. A ram (not shown) may be used to pressurize fluid 14. The conical die surface 20 makes an angle a with the axis of the die. The radial pressure P acts on the circumferential surface of the billet to cooperate with the axial pressure in pressurizing the billet. While the foregoing generally describes hydrostatic extrusion, there are many refinements known to those skilled in the art.

As in any extrusion, when the stresses in a billet are unequal, and the disparity exceeds the yield stress of the billet material, extrusion occurs. As pointed out in US. Pat. No. 3,451,24l, issued June 24, 1969 and assigned to the same assignee, the required stresses may be supplied almost totally by the radial stress component rather than by a combination of radial and axial components. The basic criteria for yield is, however, invariant.

It is not difficult to deduce that the total amount of energy or work expended in deforming the workpiece in known hydrostatic extrusion methods is the sum of several factors: First, there is the energy necessary to push the billet through the die F,, equal to the pressure P times the cross-sectional area of the billet times the rate of billet movement. Next, there is the energy due to radial pressure P Then, there is the friction of billet-against-die which must be overcome. Lastly, there is the so-called redundanf energy that is expended in abruptly changing the direction of flow of the billet, first as it starts to deform and again as it reaches the exit of the die. It will be appreciated that the magnitude of the last factor is a function of the die angle, the strain rate, and the properties of the material being extruded (i.e., lead extrudes easier than beryllium). It is convenient to set the foregoing down as the basic equation for performing the work (W) of extrusion:

mml push llutd h'ictlan redundant [It is to be noted that all equations used herein are algebraic, and factors may represent positive or negative quantities].

In a perfect or ideal system there would be no friction and no redundant work. For such a system, the following expression would be valid:

iden! vuah fluld It is not necessary to consider the total work of deformation required to extrude a billet. Rather, the work necessary to deform the billet as it moves between two points in the die is considered. Such an incremental approach is required by the fact that, as the billet deforms, its yield stress changes, as fully set forth below. Combining equations (1) and (2) for an arbitrary portion of the die results in the following expression:

torul ideal hlctiun redundmu The present invention is based, at least in part, on the proposition that, for a given billet material, desired reduction in area (i.e., extrusion ratio) and desired strain rate, there exists an optimum design of a deforming agency, in the present case a fluid control element. This in fact is the case, as set forth below, wherein there is described an optimum positive fluid flow deforming agency comprising a fluid control element having a passage extending therethrough, the surface of which passage defines a flow control surface for controlling the flow of extrusion fluid passing through the fluid control element with the material being deformed.

The factor Wmdundm was defined above with respect to hydrostatic extrusion as the energy expended in abruptly changing the direction of flow of the metal as it enters and leaves the die. In the fluid control element of the invention, however, the factor approaches zero in the crude design (a collection of segments of the flow control surface of the fluid control element) and is zero in the actual fluid control element. However, it should be noted that some workers also consider shear in the gliding mode as redundant work. Gliding shear is shear caused by the relatively different longitudinal motion of adjacent metal particles as they pass through a deforming agency. It can be shown with precision that this type of shear has exactly two-thirds the value in an optimumfluid control element that it has in a straight fluid control elementor comparable straight die.

In operation of the invention, it is essential that the fluid pass through the fluid control element with the workpiece, a concept broadly disclosed in copending US. application Ser.

No. 862,677, as noted above. This reduces the factor W by such an amount as compared to ordinary hydrostatic extrusion, that while not entirely eliminted, it is so low that fluid control elements structured according to this concept may, for friction analysis, be considered optimum. In other words, by eliminating W (as defined) entirely and by substantially eliminating W the energy necessary to carry out extrusion by this method, W will approach W,,,,.,,,. This represents an improvement of about 10-15 percent over the W necessary for conventional hydrostatic extrusion.

In prior art extrusion methods, the billet material near the surface is deformed much more than material located on or near the axis, i.e., deformation is not homogenous. When extruding with the fluid control element of the present invention, on the other hand, deformation is much more homogenous. This fact has certain practical benefits.

The fluid control element of the invention requires that there be a clearance between the billet and the flow control surface of the fluid control element, which clearance is occupied by fluid at a specific pressure, and which fluid moves through the fluid control element with the billet. At any point in the zone of deformation, i.e., that portion of the fluid control element wherein deformation occurs, the cross-sectional area occupied by the fluid is about 3 to 10 percent. Thus, the invention comprises not only the fluid control element itself, but also the method of extruding a billet therewith. Generally speaking, it can be stated that there is no metal-to-metal contact between the billet and the flow control surface during extrusion by this invention; but, this statement needs to be qualified. At each point in the fluid control element a critical clearance dimension (t) is provided between the billet and the flow control surface. This dimension gets smaller as the diameter of the passage defined by the flow control surface gets smaller, although the proportion of the cross-sectional area occupied by the fluid remains constant. From studies of fluid distribution and friction measurements, it can be said with certainty that there is no contact between the material being deformed and the flow control surface when 5 10 mils. It can be said with equal certainty that there will be effective metal contact if the fluid layer is less than about 6 microns, i.e. t 6,u.. By effective metal contact" is meant that the materials will behave as if in contact (particularly in friction) whether or not billet atoms are actually scraping flow control surface atoms. This is because a fluid layer this thin, under extrusion conditions, will behave as if it were part of the fluid control element. The actual value for I will in many instances be an intermediate figure, i.e. 10 mils t 6p.. When surface imperfections and irregularities of an ordinary billet are considered, it is not possible to entirely rule out efiective metal contact since the absolute value of t will be large, relatively, at the entrance to the zone of deformation and small at the exit. However, it can be said that, generally, there will not be effective metal contact during extrusion according to the invention.

Broadly speaking, the fluid control element of the present invention has a flow control surface, the profile of which is S shaped or sigmoidal, with zero entrance and exit angles. In a conventional or straight extrusion die, the angle a made by the sloping die surface with the die axis is, of course, a constant. While many factors go into calculating the best die angle for a given (conventional) extrusion, the maximum die angle must in any case be less than the value where the material being extruded will be subject to axial void formation, champfering, so-called dead zones" or similar problems (see, in this connection, Avitzur, Analysis of Central Bursting Defects in Extrusion and Wire Drawing," J. Eng. For Industry, ASME PaperNo. 67 Prod 5 and Flow Characteristics Through Conical Converging Dies, ASME Trans, Nov. 1966, pp. 410-420). In a sigmoidal die the die angle (surface angle in the fluid control element of the invention) varies continuously with distance from either end, having a maximum a at some intermediate point. This surface angle a m cannot be any greater in the fluid control element of the present invention that it could be in a conventional die due to the aforementioned material limitations.

While the optimum flow control surface has a smooth, S- shaped profile, it is designed as a series of discrete, frustoconical segments, each having specific radii and a specific surface angle a. The given" information that one needs to design the fluid control element is (a) properties of the materialto be extruded, (b) the billet size and feed rate, and (c) the extrusion ratio. Certain information regarding the fluid used may also be required, depending on the method of calculation. The billet size and the extrusion ratio determine only the size of the billet going in and the size of the rod or wire coming out, and do not given any information about the fluid control element size. However, it is possible to assemble a number of frustro-conical segments that approximate the flow control surface configuration, providing it is understood that the radii and surface angles for each segment are initially unknown. Design of the flow control surface involves complete calculation of extrusion conditions at each of these segments. These calculations will produce a surface angle for that segment and a necessary clearance 1 between the billet and the flow control surface. With the slope and clearance at each segment in hand, the flow control surface is completely defined. By drawing a smooth curve through the points thus produced, the design is, in effect, integrated, i.e., the number of segments becomes infinite. The profile of the flow control surface is thus established, and the fluid control element maybe manufactured from appropriate material, the opening being a revolution of the flow control surface profile about the central axis.

As noted above, the factor Wmdundm approaches zero in the design of the optimum fluid control element (the collection of segments) and is zero in the element itself. This will now be explained. The factor Wmmdm is the work it takes to change the direction of flow of the metal. In a straight fluid control element or die, this occurs at the entrance and exit of the zone of deformation. With reference to FIG. 2, it can be shown by single vector analysis that for the total force F pushing on the surface n+1 of the segment, there is a component tending to deform the workpiece P and a shear component pushing against the die, i.e., redundant work (F,). The same is true, of course, in a straight die. As shown in FIG. 2, these two force components subtend an angle 0. The relation between F, F,, is obviously defined by Sin 0 which, for convenience, is plotted in FIG. 3, i.e., the classic sine curve. It can be seen from FIG. 3 that, if 0 is kept at a value of 45 or less, the value of Sin 0 is negligible. For two given adjacent segments, then, if the difference A0 between their respective 0s is less than about 45, the value of F, will be negligible and, hence, the value of Wredundm in equation (I) will be negligible. In face, it is preferred that 0 not exceed 23.

It will be appreciated that the limiting value of A0 is for metal at the surface of the billet. On any given cross section of the billet, the value of 0 is always zero on the axis and increases with radial distance from the axis. Thus, if A0 is always less than the limiting value at the surface, it must always be less than this for the bulk of the material. For this reason, the value of 0 at the billet surface for any given segment is equal to the flow control surface angle for that same segment.

The foregoing is easier to understand if segment 1 (FIG. 4) is first considered. If segment I is really the exit of the zone of deformation where no work is done, it is parallel to the axis, and 0 0. In segment 2, if 0 3, the change in flow direction (A0) as the metal moves from segment 2 into segment I is 3, and the value of Wmundnn in making this change is negligible. In segment 3, if 0 6, A0 from segment 3 into segment 2 is only 3, so again the value of Wmmmm is negligible, and so on. When a smooth curve is drawn through all of the points, in effect making the number of segments very large, A0 for any two segments is in fact zero.

As used herein, the expression abrupt change of flow direction" is defined as meaning a A0 in excess of the prescribed limit, i.e. 45.

In practice, the individual segments are of an initial, arbitrary thickness, although it is convenient to provide more and thinner segments at the entrance end where it is known that yield stress will increase rapidly. In any event, if the calculations indicate a A0 greater than 4-5 for any two adjacent segments, the thickness of the segment is reduced until A0 is less than 4-5. As will be clear hereafter, the value of A0 must decrease near the exit end of the zone of deformation or, alternatively the thickness of a segment in this area must increase. In fact, either factor can be varied in designing the contour of the flow control surface.

It is of interest to note that, relative to conventional, straight extrusion dies, the S-shaped fluid control element is longer. Thus, it would not be practical to utilize such a deforming agency in conventional extrusion or even in ordinary hydrostatic extrusion, because the factor W would become considerably larger. With the method of the present invention, however, this factor is substantially eliminated and presents no problem. In fact, the coefficient of friction in ordinary hydrostatic extrusion of aluminum is about 0.03; in the present case it is a maximum of about 0.007.

To determine the specific angle a and clearance I for each flow control surface segment, it is first necessary to examine the material to be extruded. Essentially all crystalline materials are subject to the phenomenon of work hardening. Work hardening is defined as the rise in the yield stress with deformation. It is explained by the energy trapped as lattice strains which inevitably result from deformation. The first step in designing a fluid control element, therefore, is to determine the effective yield stress (0' eff) of the material to be extruded at a sufficient number of extrusion ratios to enable a plot of yield stress vs. reduction in area to be constructed. The plot must go from a zero reduction to at least as far as the desired reduction. One such plot is illustrated in solid line in FIG. 5, and is typical of copper and aluminum (strain is here plotted as (2) (In) Di/eD,, where Di is the diameter of a particular section). As can be seen in this instance, 0 eff builds to a maximum and then levels out. These measurements can be made on conventional hydrostatic extrusion laboratory equipment.

After the measured yield stress is plotted (the solid line in FIG. 5), it is necessary to add in corrections to take into account the effects of strain rate (the phantom line in FIG. 5).

As is discussed below, these factors, although not great, cannot properly be ignored. The completed curve, i.e. the broken line curve, is for the effective yield stress of the material.

The strain rate during extrusion is not a constant. As metal passes through an extrusion deforming agency, it obviously increases its velocity, and the strain rate of the metal increases therewith. The feed rate of the billet is a constant, however,

and this is ordinarily specified. For a given feed rate and reduction in area, the strain rate at any given segment or point in the zone of deformation may be readily calculated.

The effects of temperature and strain on the yield stress of a material may be defined by the following expression:

,those that'do have a saturation yield stress. Body-centered cubic (BCC) metals, for instance, do not exhibit this phenomena, and the equation would have to be modified therefor.

To determine numbers for these values, standard stressstrain plots are-experimentally determined over the extrusion temperature range (this is not a large range) by pulling test specimens at specific temperatures. In each test, the strain IOIMQ pelf Glad) I In this manner, Equation (4) can be solved for a sufficient number of reductions in area to plot the effective yield stress, as shown in FIG. 5.

With a plot of yield stress vs. reduction-in-area constructed, it is possible to construct a pressure profile for a conventional, straight fluid control element (where a equals, for example, 20), showing the pressure required for deformation at each segment of the zone of deformation. In calculating the values for this profile, an average value of the coefficient of friction may be used.

The necessary flow control surface clearance, t, can be derived from the balance of energy in this straight fluid control element:

AW AWrurluntlnnt AW AW l'luld null The last expression on the right of equation 5 merely accounts for any force used to pull the extruded rod or wire out of the fluid control element. Expressions for the ideal work of deformation W and redundant work Wndumm for a straight conventional die have been derived by earlier investigators (see Avitzur, Analysis of Wire Drawing and Extrusion Through Conical Dies of Large Cone Angle," J. Eng. for Industry, (ASME) Nov. 1964, pp. 305-316).

With respect to positive fluid flow extrusion, the rate of work of friction for a conical die having an inlet (i) and outlet (f), radii R, die angle a and fluid flowing at a velocity V is as follows:

friction ll+l 11 (fCOS (1) (V 1 Vf) Where f is the friction coefficient P is the fluid pressure and V is the fluid volume.

The rate of work by the fluid is:

)mm: a-m1 A where V is the volume of fluid flow. Since V is a constant through the zone of deformation, the following expression is valid:

hrura V AP F) Since P, and P, are known from the pressure profile curve, the volume of fluid in the zone of deformation can be calculated. In a zone of deformation of given length, the clearance t which this volume will occupy can be arrived at. Ordinarily, the clearance is calculated at the entrance to the zone of deformation and, since the fluid volume and its velocity are known the clearance at the exit, a smaller value, can be calculated.

The foregoing calculations illustrate how the energy balance equation may be solved for W and how the clearance I may be derived therefrom, all for a straight fluid control element of a given flow control surface angle. However, these calculations also serve as a first approximation for calculation of the actual clearance of the optimum fluid control element.

A second approximation of the optimum fluid control element is achieved by, in essence, making the same calculations for each of several segments of the flow control surface, and solving not only for the clearance I but also for the surface angle a. This is done as follows. Considering the force F as a pressure, and similarly to Equation (7), it can be shown that:

lmsll meml so it is possible to re-write Equation (5) as follows:

idenl' redundan MctlonH fluld metal F m assumed that the effective yield stress (a is a constant, os it is possible to express AF in terms of AP:

Since V and V are known from the first approximation, and since W is a function of 0:, equation (10) is solved for the value of a which gives a minimum AF (and a minimum constant). Equation (8) can now be solved for a new P, and P and a surface clearance I calculated for each segment. The improvements in going from the first approximation to the second approximation are illustrated in FIG. 8, which is a pressure profile showing curves based on (A) the first calculation and (B) the second calculation.

A third approximation, using data from the second approximation, gives even better results and a still lower pressure profile. By drawing a smooth curve through the points generated for each die segment, the actual profile of the flow control surface is generated.

One further constraint is employed in designing the optimum fluid control element: if the difference in surface angle between adjoining segments exceeds 45, the size of the segment is adjusted, so that redundant work is minimized.

The design of the optimum fluid control element need not, however, be done by a series of successive approximations. It is possible to completely calculate all factors for each segment, starting with segment 1 (FIG. 4), and then using the results to calculate for segment 2, and so forth. These calc ulations are actually very similar to the foregoing calculations, and are described with reference to segment n'below. Briefly, a value is determined for F and this is substituted into an equation for P. A value for a is assumed and values for W and W are calculated from theory. The equation for P and equation (3) are then solved, the assumed value for a being changed until equation (3) balances. The correct solution yields the proper value of a, and the correct values for P and W (this procedure is necessary because there is one more unknown than there are equations). The critical clearance l is derived from W and the flow control surface radii are thus determinable. It will be appreciated that these calculations, for each segment, would be extremely tedious without the aid of a computer, considering that values for a must be tried more or less arbitrarily, and the whole job re-calculated if A0 45 for any two segments. With a computer, the solutions are arrived at promptly.

The pressures on the segment n are shown in FIG. 2. As can be seen in this drawing, the segment has radii R,, and R,,,.,. Their difference will be referred to as AR. Force F,, acts on surface n and represents the horizontal component of the fluid force acting on the billet. Force F acts on surface n+1 and represents the total pushing force on the billet. Fluid pressures P,, and P,, act on the outside of the billet. All conditions at surface n are known: a,,, R,,, F,,, a,,, and P,,. The criteria for yield at point n+1 is defined as follows:

n+1 un n+l And, since for a segment of thickness 1,

R R, tan a,, 13.

a value for R,, is readily obtained and at the reduction in area specified by R the proper value of 01,, may be read from FIG. 5. It is to be noted that the values of R, and R, are billet radii; the radii of the flow control surface are R and R,, +t, (it is assumed constant over the segment). The complete equations for P and F,, are determined by the mechanics of the system, and are set forth below.

the calculated value for Wmm. as described previously in general terms. in particular, it is known that this value is equal In equations (l4) and it is noted that a, is any force pulling on the extruded rod, and f is the friction coefficient. Actually, it is not necessary to solve equation (14) except for checking purposes, since equation (15) can be solved and the result, containing a P expression, substituted into equation (12), and P,, determined therefrom.

With the pressure P calculated over the range 1, 2, 3...n etc., it is possible to construct a pressure profile, as shown in curve B of FIG. 8. This curve shows that the pressure rises to a point P inside the zone of deformation and then drops off to a lower value as the exit end is approached. The signiflcance of this curve is discussed below.

It is to be noted that the envelope of fluid surrounding the moving billet within the zone of deformation is, at least for small workpieces, of close to capillary size. In such a system, one would ordinarily expect a certain amount of pressure drop as fluid passed from the entrance end to the exit of the zone of deformation. It can, however, be easily demonstrated that such a natural pressure drop is negligible compared to the pressure profile set forth in FIG. 8. The natural pressure drop is measured by inserting into the fluid control element a piece of unyielding material (i.e., steel) of the exact dimensions of the billet during extrusion, holding it there while pumping fluid through thesystem under the same pressure as used for extrusion (i.e., of aluminum) and measuring the fluid pressure at the exit end of the zone of deformation.

Attention is now re-directed to equation (3). As long as the limit A0 (or Aa) 4-5 is observed, it is known that Wmmmm is negligible and can be dropped from the equation. The factor W is known from the above calculations for F. Lastly, if an arbitrary surface angle 01,, is assumed, the factors W and W can be calculated from theory. Equation 3 is now transposed into a more useful form:

There is a unique value for a that will balance equation (16) so a non-trivial solution for wflm'd is possible. 1

The calculation for W for each segment i's'based "on the theory of plasticity and has been done heretofore for a straight surface, as noted hereinabove. Essentially, it is necessary to make such a calculation for each of the segments of the flow" control surface, employing the yield stress data. A selection of a value for a is necessary to do this because the value of W varies somewhat therewith, as shown in FIG. 9. The calculation of W and W are well known and need not be detailed here, but they also vary with a, as also shown in FIG.

. 9. It is thefact that a value for a, is necessary in both these exfrom FIG. 8, it is possible to solve equation (16) for V,; translation of this volume into a frustro-conical ring of interior radii R and R, and a thickness t is simple, as set forth below.

Thus,

V,= area X velocity 17.

It is known that the fluid tends to be stationary at the flow control surface and tends to flow with the velocity of the metal at the billet wall, so the average velocity of the fluid is 0.5 of the metal velocity (v) at any given point. As a result,

and

z=D-d 19.

The segment n of the flow control surface has now beendesigned; It has a unique surface angle a and radii R and R,, +at. When each such segment is so defined, a smooth curve is drawn through all of the points, whereby the factor Wmdundm is reduced from a negligible value to zero. The flow control surface itself is constructed as a revolution of this smooth curve. The actual calculation of each segment starts at segment 1, where F is known. Calculation can start at either end of the zone of deformation or, alternatively, calculations can be made at from both ends and continued until a common 01 is reached.

From the foregoing, it can be seen that the optimum fluid control element of the invention can be designed from either a series of successive approximations starting with a straight flow control surface, or by calculating the value of W for each segment which minimizes the overall energy required. A third method may also be employed, which method is based on minimizing the entropy of the system. This method has the advantage of taking into account the viscosity of the extrusion fluid in a specific manner, in addition to the other factors discussed hereinabove. More particularly, a change in the fluid viscosity by a factor of 10 will change the clearance r by, roughly, a similar amount.

As in previously described methods, it is necessary to consider the extruding billet as a number of frusto-conical seg ments because of the non-linearity of the stress-strain relations. The yield stress of the metal and the clearance I in any segment are assumed to be constant.

If s is the length of the segment along the metal-extrusion fluid interface and r is the shear stress at the same interface, it can be shown that the rate of work of shear on the extrusion fluid, W (@qual to W is:

where d: (cosec adr cot mail-l) v velocity of the metal 41 s surface integral over the frustro-cone and H thickness of the fluid (i.e., the surface clearance). Similar expressions are derived for the rate of work due to internal deformation W,,, (equal to W,,,,,,,,), and the rate of work of the fluid W (equal to W as previously explained. The

desired surface clearance H,, is that which makes the rate of production of total entropy in the fluid control element a minimum,

Differentiating this expression, one obtains an expression for the surface clearance H in On! 11.. cos a Coseca (R 1) rod where Q is the rate of volume flow of the extrusion fluid. The optimum surface angle is therefore that angle which minimizes the increase in pressure p for the given extrusion ratio:

O i Of Once H, is determined for a segment, it may be substituted into Equation 20, and the minimization carried out to determine the optimum angle a,, for the segment.

The foregoing gives the essential equations for fluid control element design without attempting to show their derivation. A specific example of their use is illuminating.

It was desired to extrude a inch 99.99 percent aluminum billet at an extrusion ratio of 68:1 and a billet velocity of 12 inches/minute. The extrusion fluid was castor oil. The viscosity of castor oil may be expressed as i h: e t1: where 1 viscosity at room temperature and pressure 0.01 ll'l-sec/ft and== 1.01 X l'(psi)' a segment of metal near the exit end of the zone of deformation has R,, 0.026 in. R,, 002,265 in. From the pressure profile, it is determined that P 34,000 psi, and P, 29,000 psi, so that A p= 5,000 psi.

I From these equations, it is determined that 1 31 X lb-min/in 1 21.7 X 10 lb-min/in v 816 in/min 0,, 1.30 in min and (a fln 28,400 psi. Substituting this data into Equation 22, the value of H varies from 0.095 mils at the outlet of the zone of deformation to 6.51 mils at the inlet.

It is of interest to note that the mean clearance between the head of the billet and the flow control surface in the foregoing example, viz., 4.8 mils, is an order of magnitude higher than that proposed by previous workers (cf. Rozner and Faiysel, J. Franklin Institute, 1964, pp 217-236).

The value of! has been stated as being critical, and this must be quantified and explained. The calculated value oft is the unique value which will provide the value of W which satisfies equations (l)and (16). As I is increased above this value, W will increase significantly. A larger volume of pressurized extrusion fluid at a given segment or point in the fluid control element passage is going to do more work than desired. This will result in necking or uneven deformation. Conversely, a lesser volume of fluid will do less work, but this is not all: The less work that is done in a given segment, the closer the metal will come to the flow control surface, increasing the possibility of friction. The exact limits of operability for an allowable 2': t dimension are not known and will vary, obviously, with such factors as surface quality of the billet and the like. For practical purposes,'it has been determined that 25 percent is the maximum; naturally, it is desired to have t as close to the calculated value as possible.

The absolute value of twill of course vary depending on the material, fluid and extrusion parameters. It will also decrease with distance from the entrance end, as metal velocity increases. The proportion of the cross-sectional area occupied by the fluid will, however, remain constant. This proportion is about 3-10 percent generally, as well as in the specific instance set forth below.

In ordinary extrusion or even in conventional hydrostatic extrusion, deformation is not homogeneous, i.e., material at the center of the billet is not deformed as much as material near the surface. This adversely affects the physical properties of the extruded rod. When extruding with the optimum fluid control element of the present invention, however, deformation is much more homogeneous, as illustrated below. Two 99.9 percent aluminum rods of 0.360 in. initial diameter were extruded at a rate of 7 feet per minute and an extrusion ratio of slightly less than 68:1. Diameter of the extruded wire was 0.045 in. In one case, a fluid control element having a straight flow control surface was used and in the other, an optimum fluid control element according to the invention was used. Physical properties of the wires produced were as follows:

Straight Fluid Optimum Fluid Control Element Control Element Elongation, Pct. 0 96% 1.46% UltimateTensile Strength, psi. 15,050 17,900 F psi 96,000 90,800

(F is the tot pressure pushing the rod through the fluid control element).

By opening the entry angle of the fluid control element slightly, thereby flattening the pressure profile near the entrance end, F was reduced to 87,800 psi. The improved physical properties of material extruded through an optimum fluid control element are the result of the more homogeneous deformation taking place therein, and represent a significant advantage of the invention.

With reference to FIG. 8, the decrease of pressure from l to the exit end of the zone of deformation is dispositive of two further conditions: there must be a positive flow of fluid along with the metal, and the energy lost by depressurizing must be given up as work that is deforming the metal, i.e., W (it will be noted that the dimensions on both sides of equation (17) are for energy W in foot pounds, AP in lb/ft and v in ft, where lb/ft X ft lb-ft).

The actual velocity of the fluid through the zone of deformation will approach, at any given point, the velocity of the metal, and will increase across the distance I as the metal is approached. The only limit on the velocity of the fluid is that which is dictated by the Reynolds number of the fluid, which has not even been approached in practice. The fact that P is inside the zone of deformation means that fluid flowing into the fluid control element must be pumped to a slightly higher pressure to get by this point. In practice, this means that deformation of the billet until P is reached is slightly less than the calculations would indicate. This has not caused any serious problems. In the event that circumstances arise where it is a problem, the fluid control element can be opened" slightly near the entrance end so that P is leveled out between the P point and the entrance to the zone of deformation.

In the operation of the optimum fluid control element, it is 5 length of the flow control surface. Further, in the segments near the exit end, the AP per segment is quite large but the total extrusion (R R is small. There is thus more energy available than is required for the work of extrusion. It is possible, therefore, to remove a portion or even all of the fluid at this point. If all of the fluid is removed, the final section of the fluid control element becomes, in effect, a burnishing die.

In this regard, the broad concept of combining, in an extrusion deforming agency, a positive fluid flow extrusion section and a mechanical extrusion section to both deform and burnish material to form a product, comprises the subject matter of co-pending U.S.'Application Ser. No. 862,676, filed Oct. 1, i969, and assigned to the same assignee as the instant application. Additionally, the concept of extruding by a flow of pressurized fluid wherein extrusion fluid is introduced into the fluid control element within the zone of deformation is broadly disclosed in co-pending US. Application Ser. No. 862,751, filed Oct. 1, 1969, and assigned to the same assignee as the instant application.

A compound fluid control element according to the invention, i.e., a fluid control element wherein fluid is introduced within the zone of deformation and withdrawn prior to the,

completion of deformation, is illustrated in FIG. 13 wherein the fluid control element 90 is provided with a plurality of circumferential fluid inlet apertures 92 at the P point near the entrance end, and a plurality of circumferential fluid outlet apertures 94 near the exit end. It should be noted, however, that the use of a fluid control element such as that of FIG. 13 requires different extrusion apparatus than that illustrated in FIG. 12, described below, but existing extrusion equipment can be adapted for use with a compound fluid control element.

It is to be emphasized that the present invention is not to be limited in either the materials which can be treated thereby or the size of the workpiece. The design of a fluid control element will follow the same steps regardless. If a non-work hardening material is to be extruded, the yield stress will be a constant. In certain materials, the temperature and strain rate eflects will be major considerations. Further, it is to be noted that the factor W can be divided between pushing and pulling forces. It will generally be impractical to substitute pulling forces entirely, unless the reduction in area is relatively small, because W may well exceed the yield stress of the extruded rod.

Extrusion with the fluid control element of the invention requires appropriate hydrostatic equipment and requires that the fluid be supplied at the P pressure; once the fluid is working in the zone of deformation, it will, because of the design of the flow control surface, follow the plotted pressure profile. The fluid is preferably supplied at the P point but may be supplied at the entrance of the zone of deformation. This affects reduction slightly. It is to be noted that the outlet pressure (FIG. 8) is not zero. Fluid is ordinarily allowed to squirt out of the die.

Fluid which may be used to act as extrusion fluid in practicing the method of the invention may be any of those known in the art which demonstrate good pressure transmitting and flow characteristics at high pressure. With proper selection of a fluid, the work of shearing of the fluid in the fluid control element is negligible. A preferred fluid for use in the invention 1 is castor oil containing a suspension of 10 wt. pct. molybdenum disulfide (MoS While, as noted above, the invention can be applied to any solid material, a specific example should be illuminating. It was desired to extrude a 0.360 in. 99.9 percent aluminum billet with a reduction ratio of 68:1 at a billet velocity of 7 feet per minute. A fluid control element was designed and constructed in accordance with the principles of the invention. The profile thereof is illustrated in FIG. 10. It will be appreciated that while the flow control surface of the fluid control element is dimensioned as a series of frustro-conical segments, it is machined as a smooth curve. In this instance, 16 segments were employed. Dimensions of the flow control surface and material being deformed were as follows:

Overall length 0.43 in. Billet radius 0. l 8 in. Control surface radius (in) 0. l 86 In. Wire radius 0.0225 in. Control surface radius (out) 0.02355 in.

The wire was extruded using castor oil with a 10 wt. pct. suspension of M08 as the fluid, and P was 46,000 psi. The extruded wire had a bright finish.

No special materials and methods are required in manufacturing the fluid control element. Tungsten carbide is the material of choice. The flow control surface conforming to the optimum profile, is generally chromium plated to provide a smooth finish. Mounting thereof in an extrusion apparatus is discussed below.

FIG. 12 illustrates the optimum fluid control element of the invention installed in a extrusion apparatus suitable for carrying out the method of the invention; it will be appreciated, of course, that other extrusion apparatus can also be employed.

In FIG. 12, a cylindrical container 30 is provided with a cap 32 threaded into the exit end. Cap 32 has a threaded orifice 34 on the outer side for receiving a bolt 36. Bolt 36 has an axial hole 38 which allows the extruded wire 37 to exit from the machine. Bolt 36 is screwed up against an annular shoulder 40 in cap 32 which further defines a smaller orifice 42 communicating with the interior of the apparatus.

At the entrance end of container 30, a second threaded cap 44 is provided, and contains an orifice 46 for supplying extrusion fluid 48 at an appropriate pressure to the interior of the apparatus.

The interior of the apparatus comprises two main sections, a fluid control element support section 50 near the exit end and an extrusion chamber section 52 near the entrance end. Broadly, the fluid control element remains stationary while the extrusion chamber slides thereover. Fluid 48 forces the extrusion chamber to move. As it moves, extrusion chamber 52 gets smaller and extrusion proceeds.

The fluid control element support section includes a long rigid tube 54 axially located within container 30 which fits into orifice 42 of cap 32 and abuts the end of bolt 36. The opposite end of tube 54 slidably fits within opening 56 of the extrusion chamber section 52, and has the optimum fluid control element 58 axially mounted thereon. Tube 54 is supported intermediate its two ends by a plurality of telescoping supporting discs 60, which are slidably mounted within container 30 and which slidably retain tube 54 in its axial position. Rods 62 are threaded into one disc 60 and extend through openings in an adjacent disc 60 to keep the discs 60 in proper alignment. A rubber pad 64 is inserted between cap 32 and the first adjacent disc 60 to act as an impact absorber if, for any reason, extrusion section 52 pushes thereinto. A plug 66 is provided in container 30 near the exit end. This can be used to keep air from being compressed in die support section 50 during operation, and to remove any extrusion fluid 48 which seeps thereinto.

Extrusion chamber section 52 comprises a cylindrical block 68 having bushings 70 therearound for slidable engagement with the inner surface of container 30. The axial opening 56 into which tube 54 and fluid control element 58 extend runs the entire length of block 68, but is sealed with a threaded bolt 72 at the entrance end, thus defining a billet receiving chamber 73 between bolt 72 and fluid control element 58.

Oil seal rings 74, 76, 78, are provided at appropriate points.

To carry out extrusion with the apparatus of FIG. 12, cap 44 and bolt 72 are initially removed, and a billet 82 is inserted into chamber 73. The head end of billet 82 may be preshaped to more closely conform to the shape of the material during deformation. Such preparation, while desirable, is not necessary to the practice of the invention. Chamber 52 is then filled with extrusion fluid 73 and bolt 72 is replaced or bolt 72 can be replaced and fluid 73 pumped into chamber 52 through the exit end, and retained by a plug in orifice 38. Fluid 73 in chamber 52 is not initially pressurized. Cap 44 is then replaced and the system is pressurized by admission of fluid 48. As block 68 commences to slide down the interior of container 30, fluid 73 in chamber 52 is pressurized, billet 82 is forced into the zone of deformation of fluid control element 58, and extrusion proceeds as hereinabove described.

As noted above, the extrusion device of FIG. 12 would not be suitable for extrusion with the compound fluid control element of FIG. 13. An extrusion press wherein the fluid control element and extrusion chamber do not move relative to each other would be required in the latter instance, so that fluid at P pressure could be supplied through openings 92 (FIG. 13) and fluid could be removed through openings 94.

It should also be noted that the fluid control element of the invention, although described herein with respect to the extrusion of a discrete billet to form a product, may be utilized in the extrusion of a continuous rod. Specifically, the fluid control element of the invention may be utilized as the deforming agency in the apparatus disclosed in co-pending U.S. Application Ser. No. 651,292, filed July 5, 1967, and assigned to the same assignee as the present invention.

Various changes in the details, steps, materials and arrangements of parts, which have been herein described and illustrated in order to explain the nature of the invention, may be made by those skilled in the art within the principle and scope of the invention as defined in the appended claims.

I claim: 1. A method of hydrostatically deforming elongated material, said method comprising:

a. passing said elongated material through a zone of deformation defined by an extrusion die having an inlet end adapted to receive said elongated material and an outlet end adapted to discharge deformed product, passing a flow of first pressurized fluid into said zone of deformation from the inlet end of said extrusion die between said material and said extrusion die,

introducing a flow of second pressurized fluid into the zone of deformation at a point intermediate the inlet end and the outlet end of said extrusion die,

combining said flows of first and second pressurized fluids in said zone of deformation,

pressurized fluids being a maximum at the said. point within said zone of deformation at which the second pressurized fluid is introduced,

deforming said material in said zone of deformation by the exertion of pressure thereon by at least said flow of first pressurized fluid, said flow being controlled by said zone of deformation to deform said material without any abrupt change of flow direction of said material, and

g. removing a portion of said combined flows of first and second pressurized fluids from said zone of deformation between the point at which said flow of second pres surized fluid is introduced into said zone of deformation and the outlet end of said extrusion die prior to the completion of deformation of said material.

2. Extrusion apparatus for hydrostatically deforming elongated material having a head end, said apparatus comprising:

a. a chamber having an open end, said chamber being adapted to receive first pressurized fluid, said chamber being further adapted to receive said elongated material with the head end thereof facing said open end of said chamber;

b. an extrusion die associated with said chamber, said extrusion die having an inlet end facing and adapted to receive the head end of said elongated material and an outlet end adapted to discharge extruded material, said die providing a zone of deformation between said inlet end and said outlet end about said elongated material, the surface of the zone of deformation between said inlet end and said outlet end being formed with a sigmoidal profile;

. the pressure of said combined flows of first and second c. means adapted to produce a flow of first pressurized fluid into said zone of deformation from the inlet end of said extrusion die;

d. a first plurality of radially disposed openings provided in said extrusion die at a point intermediate the inlet end and outlet end of said extrusion die, said first plurality of radially disposed openings communicating with the zone of deformation;

. said first plurality of radially disposed openings being adapted to introduce a flow of second pressurized fluid into the zone of deformation at a point intermediate the inlet end and the outlet end of said extrusion die, said flow of first pressurized fluid and said flow of second pressurized fluid combining in said zone of deformation;

f. the pressure of said combined flows of first and second pressurized fluids being at a maximum at said point within said zone of deformation at which the second pressurized fluid is introduced;

g. said material being deformed at least in part in said zone of deformation by the exertion of pressure thereon by said flow of first pressurized fluid, and said material being deformed at least in part in said zone of deformation by the pressure of said combined flows of first and second pressurized fluid, said flow of first pressurized fluid and said combined flows of first and second pressurized fluids being controlled by said zone of deformation to deform said material without any abrupt change of flow direction of said material;

. a second plurality of radially disposed openings provided in said extrusion die between the point at which said first plurality of openings are formed and the outlet end of said extrusion die, said second plurality of radially disposed openings communicating with the zone of deformation; and

. said second plurality of radially disposed openings being adapted to remove aportion of said combined flows of first and second pressurized fluids from said zone of deformation between the point at which said flow of second pressurized fluid is introduced into said zone of deformation and the outlet end of said extrusion die prior to the completion of deformation of said elongated material.

3. An extrusion die for hydrostatically extruding material,

said die comprising:

a. an inlet end adapted to receive elongated material and an outlet end adapted to discharge extruded product,

b. said die providing a zone of deformation between said inlet end and said outlet end,

c. said die being adapted to encircle a portion of the length of said elongated material,

d. the surface of the zone of deformation of said die between said inlet end and said outlet end being formed with a sigmoidal profile,

e. a first plurality of radially disposed openings provided in said extrusion die at a point intermediate the inlet end and outlet end of said extrusion die, said first plurality of radially disposed openings communicating with the zone of deformation,

f. a second plurality of radially disposed openings provided in said extrusion die at a point between said first plurality of radially disposed openings and the outlet end of said die, said second plurality of radially disposed openings communicating with the zone of deformation,

g. said extrusion die being adapted to surround a flow of first pressurized extrusion fluid passing into the zone of deformation around the elongated material from the inlet end of said die,

h. said extrusion die being further adapted to surround a flow of second pressurized extrusion fluid passing into the zone of deformation around the elongated material from said first plurality of radially disposed openings, and

i. said second plurality of radially disposed openings being adapted to remove extrusion fluid from the zone of deformation. 

1. A method of hydrostatically deforming elongated material, said method comprising: a. passing said elongated material through a zone of deformation defined by an extrusion die having an inlet end adapted to receive said elongated material and an outlet end adapted to discharge deformed product, b. passing a flow of first pressurized fluid into said zone of deformation from the inlet end of said extrusion die between said material and said extrusion die, c. introducing a flow of second pressurized fluid into the zone of deformation at a point intermediate the inlet end and the outlet end of said extrusion die, d. combining said flows of first and second pressurized fluids in said zone of deformation, e. the pressure of said combined flows of first and second pressurized fluids being a maximum at the said point within said zone of deformation at which the second pressurized fluid is introduced, f. deforming said material in said zone of deformation by the exertion of pressure thereon by at least said flow of first pressurized fluid, said flow being controlled by said zone of deformation to deform said material without any abrupt change of flow direction of said material, and g. removing a portion of said combined flows of first and second pressurized fluids from said zone of deformation between the point at which said flow of second pressurized fluid is introduced into said zone of deformation and the outlet end of said extrusion die prior to the completion of deformation of said material.
 2. Extrusion apparatus for hydrostatically deforming elongated material having a head end, said apparatus comprising: a. a chamber having an open end, said chamber being adapted to receive first pressurized fluid, said chamber being further adapted to receive said elongated material with the head end thereof facing said open end of said chamber; b. an extrusion die associated with said chamber, said extrusion die having an inlet end facing and adapted to receive the head end of said elongated material and an outlet end adapted to discharge extruded material, said die providing a zone of deformation between said inlet end and said outlet end about said elongAted material, the surface of the zone of deformation between said inlet end and said outlet end being formed with a sigmoidal profile; c. means adapted to produce a flow of first pressurized fluid into said zone of deformation from the inlet end of said extrusion die; d. a first plurality of radially disposed openings provided in said extrusion die at a point intermediate the inlet end and outlet end of said extrusion die, said first plurality of radially disposed openings communicating with the zone of deformation; e. said first plurality of radially disposed openings being adapted to introduce a flow of second pressurized fluid into the zone of deformation at a point intermediate the inlet end and the outlet end of said extrusion die, said flow of first pressurized fluid and said flow of second pressurized fluid combining in said zone of deformation; f. the pressure of said combined flows of first and second pressurized fluids being at a maximum at said point within said zone of deformation at which the second pressurized fluid is introduced; g. said material being deformed at least in part in said zone of deformation by the exertion of pressure thereon by said flow of first pressurized fluid, and said material being deformed at least in part in said zone of deformation by the pressure of said combined flows of first and second pressurized fluid, said flow of first pressurized fluid and said combined flows of first and second pressurized fluids being controlled by said zone of deformation to deform said material without any abrupt change of flow direction of said material; h. a second plurality of radially disposed openings provided in said extrusion die between the point at which said first plurality of openings are formed and the outlet end of said extrusion die, said second plurality of radially disposed openings communicating with the zone of deformation; and i. said second plurality of radially disposed openings being adapted to remove a portion of said combined flows of first and second pressurized fluids from said zone of deformation between the point at which said flow of second pressurized fluid is introduced into said zone of deformation and the outlet end of said extrusion die prior to the completion of deformation of said elongated material.
 3. An extrusion die for hydrostatically extruding material, said die comprising: a. an inlet end adapted to receive elongated material and an outlet end adapted to discharge extruded product, b. said die providing a zone of deformation between said inlet end and said outlet end, c. said die being adapted to encircle a portion of the length of said elongated material, d. the surface of the zone of deformation of said die between said inlet end and said outlet end being formed with a sigmoidal profile, e. a first plurality of radially disposed openings provided in said extrusion die at a point intermediate the inlet end and outlet end of said extrusion die, said first plurality of radially disposed openings communicating with the zone of deformation, f. a second plurality of radially disposed openings provided in said extrusion die at a point between said first plurality of radially disposed openings and the outlet end of said die, said second plurality of radially disposed openings communicating with the zone of deformation, g. said extrusion die being adapted to surround a flow of first pressurized extrusion fluid passing into the zone of deformation around the elongated material from the inlet end of said die, h. said extrusion die being further adapted to surround a flow of second pressurized extrusion fluid passing into the zone of deformation around the elongated material from said first plurality of radially disposed openings, and i. said second plurality of radially disposed openings being adapted to remove extrusion fluid from the zone of deformation. 